Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.
3, 13, and 5 + 4i
A. f(x) = x4  8x3  12x2 + 400x  1599
B. f(x) = x4  200x2 + 800x  1599
C. f(x) = x4  98x2 + 800x  1599
D. f(x) = x4  8x3 + 12x2  400x + 1599
 one year ago
 one year ago
Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. 3, 13, and 5 + 4i A. f(x) = x4  8x3  12x2 + 400x  1599 B. f(x) = x4  200x2 + 800x  1599 C. f(x) = x4  98x2 + 800x  1599 D. f(x) = x4  8x3 + 12x2  400x + 1599
 one year ago
 one year ago

This Question is Closed

whpalmer4Best ResponseYou've already chosen the best response.0
We have roots of x = 3, 13, and 5+4i. We're going to need a conjugate to 5+4i also, because the complex roots come in pairs, so that will be 54i. Now the roots are simply the places where the factors of the polynomial = 0, so we can write our factored polynomial as \[f(x) = (x3)(x+13)(x54i)(x5+4i) = 0\] Now it's just some pencilpushing to multiply that expression out to get f(x) = x^4 + more terms. I would suggest multiplying the (x54i) and (x5+4i) terms first, as doing so will eliminate the terms containing i (remember that i^2 = 1).
 one year ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.